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In this paper we study fractional initial value problems with Caputo–Fabrizio derivative which involves nonsingular kernel. First we apply α - ℓ -contraction and α -type F -contraction mappings to study the existence and uniqueness of solutions for such problems. Finally, we use some contraction mappings in complete F $\mathfrak{F}$ -metric spaces for this purpose.

Application of some new contractions for existence and uniqueness of differential equations involving Caputo–Fabrizio derivative